Question

How do you write an equation for the line that passes through (4,7) and is perpendicular to the line y=2/3x-1?

Answer 1

Please see the explanation for the process. `y = -3/2x + 19`

Explanation:

The slope of the line: `y = 2/3x - 1` is `2/3`.

The slope of any line perpendicular is the negative reciprocal: `-3/2`

Use the point-slope form of the equation of a line to force the line through point `(4, 7)`:

`y - 7 = -3/2(x - 4)`

`y - 7 = -3/2x +12`

`y = -3/2x +19`